1.   Evaluate the following :
 
(i)   sin 60° cos 30° + sin 30° cos 60°            (ii)  2 tan2 45° + cos2 30° – sin2 60° 

(iii) ${cos 45° }/{sec 30° + cosec 30° }$           (iv) ${sin 30° + tan 45° – cosec  60°}/{sec 30° + cos 60° + cot 45°} $

(v) ${5 cos^2   60° +  4 sec^2   30° −  tan^2   45°}/{sin^2   30° + cos^2   30°}$
 
2.   Choose the correct option and justify your choice :

	(i) ${2 tan 30°}/{1 +  tan^2   30°} =$ 
	      (A)     sin 60°            (B)  cos 60°               (C)  tan 60°                  (D)  sin 30°
	
	(ii)${1 − tan^2   45°  }/{1 +  tan2   45°} =$
	     (A)     tan 90°           (B)  1                         (C)  sin 45°                  (D)  0 

	(iii)   sin 2A = 2 sin A is true when A =
	      (A)     0°                   (B)  30°                      (C)  45°                        (D)  60°
	
	(iv)  ${2 tan 30°}/{1 −  tan^2 30°}$=
	      (A)     cos 60°           (B)  sin 60°                (C)  tan 60°                  (D)  sin 30°
		  
3.   If tan (A + B) = √3 and tan (A – B) =$1/√3$ ; ; 0° < A + B ≤ 90°; A > B, find A and B.

4.   State whether the following are true or false. Justify your answer.
	(i)   sin (A + B) = sin A + sin B.
	(ii)   The value of sin θ increases as θ increases.
	(iii)   The value of cos θ increases as θ increases.
	(iv)   sin θ = cos θ for all values of θ.
	(v)   cot A is not defined for A = 0°.

Solution